The vertex angle of an isoceles triangle 40 degrees less than the sum of the measures of the base angles. Determine the measure of the vertex angles.

V = vertex angle

B = base angle

"the vertex angle is 40 degrees less than the sum of the measures of the base angles" means V = B+B-40 which turns into V = 2B-40

Use the fact that the three angles (B, B, V) add up to 180 degrees. Then use substitution to solve for B

V+B+B = 180

V+2B = 180

2B-40+2B = 180

4B-40 = 180

4B = 180+40

4B = 220

B = 220/4

B = 55

Each base angle is 55 degrees

V = 2B-40

V = 2*55-40

V = 110-40

V = 70

The vertex angle is 70 degrees

Check:

V+B+B = 70+55+55 = 180

answer checks out